Inverse problems of the analysis of input-output balances

The paper proposes a modification of the approach to the analysis of inter-sectoral balance. Instead of V.V. Leontiev's assumption about the constancy of the cost rates of production factors, a more realistic assumption about the constancy of the proportions of inter-industry cash flows is used in modern conditions. We propose an algorithm for solving the inverse problem that allows us to identify a model of nonlinear inter-industry balance with a utility function and production functions of Cobb-Douglas type based on the data of the symmetric input-output table. Based on the use of the Young transform and Fenchel duality, a technology for analyzing inter-sectoral relationships using this model has been developed. The technology has been tested on the data of economic statistics of Russia.